An unnamed Yoshi tech demo was unveiled at the time of the Game Boy Advance's first announcement. The title was seemingly either a port or direct sequel to Yoshi's Story, but it is unknown if it was simply meant as a demo or was cancelled. Years later, a Yoshi title called Yoshi Topsy-Turvy was released which featured the same art style and mechanics as Yoshi's Story and was perceived as a sequel. Yoshi's Story was also the first Mario/Yoshi game on the Nintendo 64 released in North America to be rated E for everyone due to the changeover by the ESRB from the previously used K-A "Kids to Adults" rating in 1998. The game sold 1.28 million copies in America and 2.85 million worldwide.

Baby Bowser has turned Yoshi's Island into a picture book and has stolen the Super Happy Tree. Six (and more to be revealed as player find the secret/hidden eggs) babyYoshis take it upon themselves to defeat him, meaning they must venture through six "pages" of the island before they can confront him. Each level is made of some kind of material (e.g., clay, denim, cardboard, newspaper, etc.) and has its own distinct style.

Yoshi's Story is played much like Super Mario World 2: Yoshi's Island, although a few aspects were tweaked or removed, such as the timer that counted down for Baby Mario when Yoshi was hit or Yoshi's ability to morph. To complete a level, the Baby Yoshis have to eat exactly thirty Fruits scattered through the level. Before starting a level, the Player has to select a Baby Yoshi. Each Yoshi has different taste when it comes to Fruits and Shy Guys and will recover more health (and score more points) if it eats a Fruit or a Shy Guy that is of its own color. The top left corner of the screen has a flower which serves as the life bar; the flower's petals will fall off as Yoshi loses more health, and its facial expression will also change accordingly (happy when full, sad when dying). Certain characters aid the Yoshis in various ways, including Miss Warp, who can teleport the Yoshis to different parts of the level, and Poochy, who can find hidden objects from far away.

If a Baby Yoshi is defeated within the level, this Baby Yoshi will be taken to Bowser's Castle by Baby Bowser's Toadies. If all of the Baby Yoshis are kidnapped, the game is over. However, any lost Baby Yoshi (aside from the secret, unlockable Black and White Yoshis) can be saved by finding a White Shy Guy and finishing the level with it. When starting a game on either Story Mode or Trial Mode, the game will randomly select a "Lucky Fruit". Said Lucky Fruit automatically heals all of the Yoshi's life, even if the Yoshi is not supposed to like the fruit.

Each world has four different levels to chose from; once beaten, the player moves on to the next world, without visiting the other three levels. This means to play through every single level, the player must play through the game at least four different times, going to the unvisited levels in each world. The game has four different difficulty levels: novice, easy, medium, and hard.

The main cast of Yoshi's Story, featuring the eight Yoshis that appear in the game as well as Poochy.

The main portion of the game, the Story Mode contains 24 levels (four per world), but only six can be played during a single playthrough (the game jumps directly to the next world after a level is completed). The player can choose which of the four levels in page one they wish to start on. However, the choice of levels in later worlds is determined by the number of Special Hearts collected in the previous level. To finish each level, the Yoshis must eat 30 different fruits scattered throughout the level. Whenever a level is completed, the Baby Yoshis start singing and a text appears to explain what happened in the level.

Trial Mode is a mode that allows the player to play any stage that they have beaten in the Story Mode. In order to unlock all the stages, the players must play the Story Mode at least 4 times and get all the Special Hearts from the stage that they were playing. This mode was created to save the player's highest score of the levels. To quit a stage, the + buttons should be pressed together. Also, the player can't use Black Yoshi and White Yoshi; those are only playable in the Story Mode.

Eating nothing but melons is a great method of increasing one's high score, although it can be really difficult to perform in some stages. If this is done, a marker appears at the end of the level. In order to eat all the melons from the stage, the player will need to Sniff-Sniff all the time to find hidden objects in the ground.

Also, if the player waits for two minutes and ten seconds, Totaka's Song is heard.

By pressing the A button, the player can make Yoshi jump; by pressing A again and holding it, the player can make a Yoshi Flutter Jump. This helps the player get to higher places. It is possible to flutter longer by holding A after Yoshi grunts.

To Swallow an object, the Baby Yoshies have to lick with their tongues. It is possible to control the direction of the tongue with the Control Stick. Unlike Yoshi’s Island, Yoshi automatically ingests the things he eats with his tongue.

To utilize this move, a Baby Yoshi must jump and quickly press down on the control stick. The Yoshi will pound the ground. A Ground Pound can be used to reveal a few items hidden in the ground or to defeat enemies.

A move exclusive to this game, Sniff-Sniffing is helpful in finding objects hidden in the ground. To execute it, the player must press R. If the Baby Yoshi is near an object, a ! will appear next to the Baby Yoshi's head. If Baby Yoshi is standing on a hidden item, he will wave at the player. Any objects hidden in the ground can be revealed by ground-pounding them. Poochy can be found in a few levels and will sniff for the Yoshi Clan.

All the following Yoshis are playable. Their name is listed next to what their favorite fruit in the game is (since when a Yoshi eats one of its favorite food, the life bar heals more than it usually would). Eaten Melons will also have this effect, no matter which Yoshi color it is.

Yoshi's Story is notable for being one of the very few Yoshi games to not involve Mario. Both Mario and Luigi are only briefly mentioned on newspaper headlines in the background of level 2-3 and 2-4. Baby Bowser also calls Yoshi "Mario's pet".

The Japanese box art is very similar to the cover of the American game booklet.

When the page turns, the player can hear the Baby Yoshis singing "Nintendo" in the background.